I never put my LO on her side, it just didn't seem to work well for us. I just pat her gently on her chest when I started, but now I just have a firm hand on her chest, and sometimes rub her head while also blocking out visual stimulation. I have my head near her head and shssh if needed (we don't need the sound too much anymore).
Sometimes, I did have to hold her legs down too, she liked to rub them together, and this stimulated her. I think the key with shssh/pat is do what works for your LO and you, and keep it consistent. So if putting him on his side doesn't work, try another method.